A smooth particle-mesh Ewald algorithm for Stokes suspension simulations: The sedimentation of fibers

Large-scale simulations of non-Brownian rigid fibers sedimenting under gravity at zero Reynolds number have been performed using a fast algorithm. The mathematical formulation follows the previous simulations by Butler and Shaqfeh f“Dynamic simulations of the inhomogeneous sedimentation of rigid fibres,” J. Fluid Mech. 468, 205 s2002dg. The motion of the fibers is described using slender-body theory, and the line distribution of point forces along their lengths is approximated by a Legendre polynomial in which only the total force, torque, and particle stresslet are retained. Periodic boundary conditions are used to simulate an infinite suspension, and both far-field hydrodynamic interactions and short-range lubrication forces are considered in all simulations. The calculation of the hydrodynamic interactions, which is typically the bottleneck for large systems with periodic boundary conditions, is accelerated using a smooth particle-mesh Ewald sSPMEd algorithm previously used in molecular dynamics simulations. In SPME the slowly decaying Green’s function is split into two fast-converging sums: the first involves the distribution of point forces and accounts for the singular short-range part of the interactions, while the second is expressed in terms of the Fourier transform of the force distribution and accounts for the smooth and long-range part. Because of its smoothness, the second sum can be computed efficiently on an underlying grid using the fast Fourier transform algorithm, resulting in a significant speed-up of the calculations. Systems of up to 512 fibers were simulated on a single-processor workstation, providing a different insight into the formation, structure, and dynamics of the inhomogeneities that occur in sedimenting fiber suspensions. © 2005 American Institute of Physics. fDOI: 10.1063/1.1862262g